1. Field of the Invention
The invention relates to methods and systems for determining an inverse filter for altering a loudspeaker's frequency response in an effort to match the output of the inverse-filtered loudspeaker to a target frequency response. In typical embodiments, the invention is a method for determining such an inverse filter from measured, critically banded data indicative of the loudspeaker's impulse response in each of a number of critical frequency bands.
2. Background of the Invention
Throughout this disclosure including in the claims, the expression “critical frequency bands” (of a full frequency range of a set of one or more audio signals) denotes frequency bands of the full frequency range that are determined in accordance with perceptually motivated considerations. Typically, critical frequency bands that partition an audible frequency range have width that increases with frequency across the audible frequency range.
Throughout this disclosure including in the claims, the expression “critically banded” data (indicative of audio having a full frequency range) implies that the full frequency range includes critical frequency bands (e.g., is partitioned into critical frequency bands), and denotes that the data comprises subsets, each of the subsets consisting of data indicative of audio content in a different one of the critical frequency bands.
Throughout this disclosure including in the claims, the expression performing an operation (e.g., filtering or transforming) “on” signals or data is used in a broad sense to denote performing the operation directly on the signals or data, or on processed versions of the signals or data (e.g., on versions of the signals that have undergone preliminary filtering prior to performance of the operation thereon).
Throughout this disclosure including in the claims, the expression “system” is used in a broad sense to denote a device, system, or subsystem. For example, a subsystem that determines an inverse filter may be referred to as an inverse filter system, and a system including such a subsystem (e.g., a system including a loudspeaker and means for applying the inverse filter in the loudspeaker's signal path, as well as the subsystem that determines the inverse filter) may also be referred to as an inverse filter system.
Throughout this disclosure including in the claims, the expression “reproduction” of signals by speakers denotes causing the speakers to produce sound in response to the signals, including by performing any required amplification and/or other processing of the signals.
Inverse filtering is performed to improve the listening impression of one listening to the output of a loudspeaker (or set of loudspeakers), by canceling or reducing imperfections in an electro-acoustic system. By introducing an inverse filter in the loudspeaker's signal path, a frequency response that is approximately flat (or has another desired or “target” shape) and a phase response that is linear (or has other desired characteristics) may be obtained. An inverse filter can eliminate sharp transducer resonances and other irregularities in the frequency response. It can also improve transients and spatial localization. In traditional techniques, graphic or parametric equalizers have been used to correct the magnitude of loudspeaker acoustic output, while introducing their own phase characteristics on top of the preexisting loudspeaker phase characteristics. More recent methods implement deconvolution or inverse filtering which allows for correction of both finer frequency resolution as well as phase response. Inverse filtering methods commonly use techniques such as smoothing and regularization to reduce unwanted or unexpected side effects resulting from application of the inverse filter to the acoustic system.
A typical loudspeaker impulse response has large differences between the maxima and minima (sharp peaks and dips). If the loudspeaker response is measured at a single point in space, the resulting inverse filter will only flatten the response for that one point. Noise or small inaccuracies in the impulse response measurement may then result in severe distortion in a fully inverse filtered system. To avoid this situation, multiple spatial measurements are taken. Averaging these measurements prior to optimizing the inverse filter results in a spatially averaged response.
It is crucial to apply inverse filtering moderately so that loudspeakers are not driven outside their linear range of operation. An overall limit on the amount of correction applied is considered a global regularization.
To avoid dramatic or narrow compensation it is possible to use frequency dependent regularization in the computations, or otherwise perform frequency-dependent weighting of values generated during the computations (e.g., to avoid compensating for deep notches where it would be undesirable to do so). For example, U.S. Pat. No. 7,215,787, issued May 8, 2007, describes a method for designing a digital audio precompensation filter for a loudspeaker. The filter is designed to apply precompensation with frequency-dependent weighting. The reference suggests that the weighting can reduce the precompensation applied in frequency regions where the measuring and modeling of the loudspeaker's frequency response is subject to greater error, or can be perceptual weighting which reduces the precompensation applied in frequency regions where the listener's ears are less sensitive.
Until the present invention, it had not been known how to implement critical band smoothing efficiently during inverse filter determination. For example, it had not been known how to implement a method for determining an inverse filter for a loudspeaker in which critical band smoothing is performed on the speaker's measured impulse response during an analysis stage of the inverse filter determination, and the inverse of such critical band smoothing is performed during a synthesis stage of the inverse filter determination on banded filter values to generate inverse filtered values that determine the inverse filter.
Nor had it been known until the present invention how to perform inverse filter determination efficiently, including by applying eigenfilter theory (e.g., including by expressing stop band and pass band errors as Rayleigh quotients), or by minimizing a mean square error expression by solving a linear equation system.